// Numbas version: exam_results_page_options
{"name": "cormac's copy of Apply the sine rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "variables": {"t0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "t0", "definition": "sin(bb0)"}, "a3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "a3", "definition": "random(10..25)"}, "q3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "q3", "definition": "(a3^2+c3^2-b3^2)/(2*a3*c3)"}, "p0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "p0", "definition": "(c0^2+b0^2-a0^2)/(2*c0*b0)"}, "c02": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c02", "definition": "floor(max(a0+0.9*b0,b0+0.9*a0))"}, "aa4": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "aa4", "definition": "pi-BB3-CC3"}, "u3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "u3", "definition": "sin(CC3)"}, "aa5": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "aa5", "definition": "precround(AA4,3)"}, "cc1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "cc1", "definition": "//Angle C calculated from A,B\n    pi-aa0-bb0"}, "r3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "r3", "definition": "(a3^2+b3^2-c3^2)/(2*a3*b3)"}, "c0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c0", "definition": "random(c01..c02)"}, "bb0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "bb0", "definition": "//The angle B\n    precround(arccos(q0),4)"}, "bb1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "bb1", "definition": "//Angle B calculated from A,C\n    pi-aa0-cc0"}, "t2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "t2", "definition": "sin(bb2)"}, "check": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "check", "definition": "pi-AA0-BB0-CC0"}, "aa1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "aa1", "definition": "//Angle A calculated from B,C\n    pi-bb0-cc0"}, "t3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "t3", "definition": "sin(BB3)"}, "check2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "check2", "definition": "pi-AA3-BB3-CC3"}, "r0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "r0", "definition": "(a0^2+b0^2-c0^2)/(2*a0*b0)"}, "c01": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c01", "definition": "ceil(sqrt(a0^2+b0^2))+1"}, "s2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s2", "definition": "sin(aa2)"}, "c3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c3", "definition": "random(c31..c32)"}, "u0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "u0", "definition": "sin(cc0)"}, "c32": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c32", "definition": "floor(max(a3+0.9*b3,b3+0.9*a3))"}, "bb2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "bb2", "definition": "precround(bb1,3)"}, "aa0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "aa0", "definition": "//The angle A\n    precround(arccos(p0),4)"}, "a0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "a0", "definition": "random(10..25)"}, "aa3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "aa3", "definition": "precround(arccos(p3),4)"}, "s5": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s5", "definition": "sin(AA5)"}, "cc2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "cc2", "definition": "precround(cc1,3)"}, "cc4": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "cc4", "definition": "pi-AA3-BB3"}, "bb4": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "bb4", "definition": "pi-AA3-CC3"}, "s3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s3", "definition": "sin(AA3)"}, "t5": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "t5", "definition": "sin(BB5)"}, "c31": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c31", "definition": "ceil(sqrt(a3^2+b3^2))+1"}, "b0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "b0", "definition": "random(14..30)"}, "bb3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "bb3", "definition": "precround(arccos(q3),4)"}, "cc0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "cc0", "definition": "//The angle C\n    precround(arccos(r0),4)"}, "bb5": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "bb5", "definition": "precround(BB4,3)"}, "b3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "b3", "definition": "random(13..29)"}, "u5": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "u5", "definition": "sin(CC5)"}, "q0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "q0", "definition": "(a0^2+c0^2-b0^2)/(2*a0*c0)"}, "cc3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "cc3", "definition": "precround(arccos(r3),4)"}, "u2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "u2", "definition": "sin(cc2)"}, "aa2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "aa2", "definition": "precround(aa1,3)"}, "cc5": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "cc5", "definition": "precround(CC4,3)"}, "p3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "p3", "definition": "(c3^2+b3^2-a3^2)/(2*c3*b3)"}, "s0": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s0", "definition": "sin(aa0)"}}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "ungrouped_variables": ["s3", "cc0", "b0", "cc3", "b3", "cc2", "check", "q0", "q3", "cc5", "s2", "s0", "cc1", "u0", "u3", "u2", "aa5", "aa4", "aa1", "aa0", "aa3", "aa2", "c31", "c32", "a0", "a3", "s5", "c3", "c0", "c02", "p3", "p0", "r0", "r3", "bb3", "t5", "t2", "t3", "t0", "u5", "cc4", "c01", "bb5", "bb4", "check2", "bb2", "bb1", "bb0"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Two questions testing the application of the Sine Rule when given two angles and a side. In this question the triangle is obtuse. In one question, the two given angles are both acute. In the second, one of the angles is obtuse.</p>"}, "name": "cormac's copy of Apply the sine rule", "extensions": [], "variable_groups": [], "advice": "<p>a) We use the Sine Rule to find $b$: $\\dfrac{a}{\\sin A}=\\dfrac{b}{\\sin B}$. Thus $b=\\dfrac{a \\sin B}{\\sin A}=\\dfrac{\\var{a0}* \\var{t0}}{\\var{s0}}=\\var{a0*t0/s0}$. The closest integer is then $\\var{b0}$.</p>\n  <p>Since $A+B+C=\\pi$, we calculate $C=\\pi-A-B=\\var{CC1}$. To 3dp, this gives $\\var{CC2}$.</p>\n  <p>We use the Sine Rule to find $c$: $\\dfrac{a}{\\sin A}=\\dfrac{c}{\\sin C}$. Thus $c=\\dfrac{a \\sin C}{\\sin A}=\\dfrac{\\var{a0}* \\var{u2}}{\\var{s0}}=\\var{a0*u2/s0}$. The closest integer is then $\\var{c0}$. Note that this solution uses the 3dp value of $C$; the answer using $\\var{CC1}$ would give a slightly different long decimal value of $c$, but the integer value would be the same.</p>\n  <p>b) We use the Sine Rule to find $b$: $\\dfrac{b}{\\sin B}=\\dfrac{c}{\\sin C}$. Thus $b=\\dfrac{c \\sin B}{\\sin C}=\\dfrac{\\var{c3}* \\var{t3}}{\\var{u3}}=\\var{c3*t3/u3}$. The closest integer is then $\\var{b3}$.</p>\n  <p>Since $A+B+C=\\pi$, we calculate $A=\\pi-B-C=\\var{AA4}$. To 3dp, this gives $\\var{AA5}$.</p>\n  <p>We use the Sine Rule to find $a$: $\\dfrac{a}{\\sin A}=\\dfrac{c}{\\sin C}$. Thus $a=\\dfrac{c \\sin A}{\\sin C}=\\dfrac{\\var{c3}* \\var{s5}}{\\var{u3}}=\\var{c3*s5/u3}$. The closest integer is then $\\var{a3}$. Note that this solution uses the 3dp value of $A$; the answer using $\\var{AA4}$ would give a slightly different long decimal value of $a$, but the integer value would be the same.</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "parts": [{"showCorrectAnswer": true, "prompt": "<p>$A=\\var{AA0}$, $B=\\var{BB0}$, $a=\\var{a0}$</p>\n      <p>Side length $b=$ [[0]]</p>\n      <p>Angle $C=$ [[1]]</p>\n      <p>Side length $c=$ [[2]]</p>", "customMarkingAlgorithm": "", "gaps": [{"mustBeReducedPC": 0, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "marks": 1, "variableReplacements": [], "type": "numberentry", "minValue": "{b0}", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "unitTests": [], "correctAnswerFraction": false, "allowFractions": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "maxValue": "{b0}", "correctAnswerStyle": "plain"}, {"strictPrecision": true, "customMarkingAlgorithm": "", "precisionType": "dp", "marks": 1, "variableReplacements": [], "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "precision": 3, "correctAnswerStyle": "plain", "precisionPartialCredit": 0, "allowFractions": false, "scripts": {}, "maxValue": "{CC2}+0.001", "showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "minValue": "{CC2}-0.001", "mustBeReduced": false, "unitTests": [], "correctAnswerFraction": false, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true}, {"mustBeReducedPC": 0, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "marks": 1, "variableReplacements": [], "type": "numberentry", "minValue": "{c0}", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "unitTests": [], "correctAnswerFraction": false, "allowFractions": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "maxValue": "{c0}", "correctAnswerStyle": "plain"}], "marks": 0, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "unitTests": [], "sortAnswers": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true}], "statement": "<p>Suppose that $\\Delta ABC$ is a triangle with $C&gt; \\dfrac{\\pi}{2}$ (so it is an obtuse triangle). Here all angles are expressed in radians. Suppose also that standard naming conventions are used (i.e. the sides opposite angles A,B and C are called a,b and crespectively).&nbsp;</p>\n<p style=\"margin: 0px;\">Given the following two angles and a side length, determine the other two side lengths and the angle. Write down the side lengths as whole numbers and the angle (in radians) as a decimal to 3dp.</p>\n<p style=\"margin: 0px;\"></p>\n<p style=\"margin: 0px;\"></p>", "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "cormac breen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/306/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "cormac breen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/306/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}